1. Let A, B and C be the subsets of U. Then prove that (A – B) - (B - C) = A-B by using laws of sets

Q: Let A, B, C be three non-empty sets. Suppose that A× C = B× C. Prove that A = B

A: Here given that A, B, C be three non-empty sets. And suppose that A×C=B×C. We have to prove that…

Q: 4- A subset [a, b] R is compact set in: a- (R, Td), b- (R, T), c-Both (R, Tu) and (R, T₁) d- No one.…

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

Q: Prove that if A and B are transitive sets, then A ∪ B and A ∩ B are transitive sets

A:

Q: 2. Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly?

A: No, there is no set A that satisfies A={A}. Let A is an empty set, i.e.  A=  or  A=ϕ, in which…

Q: Let A, B and C be overlapping sets, verify following by using Venn diagram and membership table ((An…

A: Consider the provided question,

Q: Prove that if A and B are sets, then P(A) U P (B) C P(AUB).

A:

Q: Suppose A, B and C are sets. Prove that if A ⊆ B, then A - C ⊇ B - C

A: Dear student in the question we can't prove,  Suppose A, B and C are sets. Prove that if A ⊆ B, then…

Q: Let C, D be subsets of a set U. By proving two inclusions, show that (CC n D) U (C n D) = D where Ce…

A:

Q: Show that if A and B are sets with AS B, then a) A UB-B. b) ANB-A.

A: Let A and B are two sets with A⊆B a) Let x∈A∪B which implies that x∈A or x∈B. Hence we can imply…

Q: Prove that for sets  A and B,  we have  (A∪B)−(A∩B)=A−B if and only if B⊂A.

A: By theorem we know that,            A⊂B if and only if A∩B =A and  A∪B =B

Q: Answer the following questions by replying to this post. Given that the elements of the sets A, B,…

A: As per the company guidelines we can solve first three parts of question. I hope that the given…

Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

A:

Q: Let A and B be two subsets of E. Prove using the set identities: А - В — В — А.

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: . Let A and B be two connected subset

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the set M = {m,a,{t,h},e,m,{a,t,î},c,s}. 1. What is the cardinality of M?

A: M = { m,a, {f,h} , e,m, {a1, i} ,e ,s}1. Carbimalty of M = 72. No, {m,a,f,h} is not a properSubser…

Q: Show that every open set with respect to 7 is a union of open ball(s).

A:

Q: Let A, B and C be the subsets of U. Then prove that (A UB) – C = (A – C) U(B – C) by using laws of…

A: I have just used the law of sets

Q: Prove formally that A\ B= A\(An B), for any sets A and B.

A:

Q: If sets X and Y are countable, then prove or disprove that X-Y is uncountable.

A:

Q: Disprove the following statement by finding a counterexample. For all sets A, B, and 6, C, An (BUC)…

A:

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a,b) : a € A…

A:

Q: Let C and D are be the subsets of some universal set U. Then D-C = C'nD is

A: We have to identify the statements as true or false.

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

A:

Q: Let A and B be sets. Prove that the intersection of A and B is is a subset of the union between A…

A: To show that the elements which are common to both A and B belong to either A or B.

Q: 4. By the use of Venn diagrams, in which the space C is the set of points enclosed by a rectangle…

A:

Q: 4. Let A and B be sets, prove that P(A)UP(B) C P(AUB).

A:

Q: Let C, D be subsets of a set U. By proving two inclusions, show that (Cºn D) U (C N D) = D where CC…

A: Identities of the sets

Q: If a finite set A equals the union of k subsets A1, A2,..., Ak, then the number of elements in A…

A:

Q: Prove that if A and B are sets, then (A∩B)∪(A∩B^' )=A

A: To prove : A∩B∪A∩B'=A   Let x∈A∩B∪A∩B' ⇒x∈A∩B or x∈A∩B' ⇒x∈A and x∈Bor x∈A and x∈B' In either of the…

Q: Prove the following theorem directly. 'Let B, E,W be sets. If B Ɔ W, then BU E WUE"

A: Given B, E and W are three sets .

Q: 1. Prove that, if A, B, and C are sets and if ACB and ACC, then ACBOC.

A: To prove: A⊆B∩C

Q: If A and B are sets and A is a subset of B, then A and B cannot be disjoint.

A:

Q: Let C, D be subsets of a set U. By proving two inclusions, show that (C° n D) U (Cn D)= D where Ce…

A:

Q: Prove that for all sets A, B, and C, if CCB-A, then AnC=0.

A:

Q: Prove that if A and B are sets, then A - B = An BC.

A:

Q: 1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a…

A: This question is related to Set theory, We will solve it using given information.

Q: Suppose A, B, and C are sets, A. Prove that: Ax (Bn C) = (A × B) n (A × C) %3D Using Membership…

A:

Q: If A is a countable set and B is a subset of A then

A: If A is a countable set and B is a subset of A then B is also a countable set since, every subset of…

Q: Draw a Venn diagram for the symmetric difference of the sets A and B.

A:

Q: Let A, B and C be the subsets of U. Then prove that (A UB) -C = (A – C)U(B – C) by using laws of…

A: 1) It is the question of computer science.

Q: 1. Prove the following statements about sets A and B. A B= AN Bº %3D

A: Given: Let A and B be two sets. To prove,A-B=A∩Bc

Q: Draw a venn diagram to represent the set A insersects B, but B has a line over it showing its a…

A: To represent the given combination of sets (A intersection B complement) in a Venn diagram

Q: 2. If A, B and C are sets, use a membership table to prove or disprove: A U (B N c) = (A U B) n (A U…

A: First we prove that left hand side is subset of right hand side and then right hand side is subset…

Q: 1. Let A, B, and C be the subsets of U. Then by using laws of sets prove A-(BnC)=(A– B)U(A-C)

A:

Q: Show that the subset (a, b) of R is homeomorphic with R.

A: Recall that every nonempty open interval (a,b) is homeomorphic to the nonempty interval (c,d).

Q: Prove that if A, B.C are subsets of a universal set U, then AU(BnC) C (AUB)n(AUC)

A: use the basic property of subset and set theory.

Q: Determine whether the set S = {1, x², 9 + x²} spans P2. %3D O S spans P2. O s does not

A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…

Q: Show by membership that for all sets A, B and C: A - (AnB) CA – B

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.